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Simulation-based fast collision detection for scaled polyhedral objects in motion by exploiting analytical contact equations

Published online by Cambridge University Press:  08 August 2014

Jing-Sin Liu ,
Wen-Hua Pan ,
Wen-Yang Ku ,
Y.-H. Tsao  and
Y.-Z. Chang
Jing-Sin Liu*
Affiliation:
Institute of Information Science, Academia Sinica, Nangang, Taipei, Taiwan 115, Republic of China
Wen-Hua Pan
Affiliation:
Department of Engineering Science and Ocean Engineering, National Taiwan University, Taipei, Taiwan 105, Republic of China
Wen-Yang Ku
Affiliation:
Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON M5S 3G8, Canada
Y.-H. Tsao
Affiliation:
Department of Mechanical Engineering, Chang Gung University, Tao-Yuan, Taiwan 333, Republic of China
Y.-Z. Chang
Affiliation:
Department of Mechanical Engineering, Chang Gung University, Tao-Yuan, Taiwan 333, Republic of China
*
*Corresponding author. E-mail: liu@iis.sinica.edu.tw
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Summary

Based on the results of the study of convex object motion1 (J. Hopcroft and G. Wilfong, “Motion of objects in contact,” Int. J. Robot. Res., 4(4), 32–46 (1986)), this paper addresses the problem of exact collision detection of a pair of scaled convex polyhedra in relative motion, and determines the contact conditions of tangential contact features, arbitrary relative motion involving translation and rotation, and uniform scaling of the objects about a fixed point. We propose a new concept of the decision curve based on analytical contact equations that characterize a continuum of scaling factors (or a single scaling factor), which ensures that a pair of objects undergoing a scaling transformation will maintain the same tangential contact feature pair (or make instantaneous tangential contact feature transitions). We propose a reliable simulation-based approach to construct the decision curve by hybridizing analytical contact equations and conventional collision detection method, called the Fast Collision Detection Method (FCDM). This method can determine whether two scaled objects will make contact at specific tangential contact features (vertices, edges, or faces) under particular uniform scaling factors and after distinctive relative motion with better accuracy and less computational time than the existing collision detection methods. Finally, we demonstrate our approach for solving motion design in simple assembly/disassembly problems.

Keywords

Collision detectionContactScalingRelative motionAssembly
Type
Articles
Information
Robotica , Volume 34 , Issue 1 , January 2016 , pp. 118 - 134
Copyright
Copyright © Cambridge University Press 2014 

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References

1.Hopcroft, J. and Wilfong, G., “Motion of objects in contact,” Int. J. Robot. Res., 4 (4), 32–46 (1986).CrossRefGoogle Scholar
2.van den Bergen, G., Collision Detection in Interactive 3D Environments, Morgan Kaufmann Series in Interactive 3D Technology (Morgan Kaufmann, Burlington, MA, 2004).Google Scholar
3.Ericson, C., Real-Time Collision Detection (Elsevier, Philadelphia, PA, 2005).Google Scholar
4.Lin, M. and Gottschalk, S., “Collision detection between geometric models: A survey,” Proceedings of the IMA Conference on Mathematics of Surfaces, Vol. 1 (1998) pp. 602–608.Google Scholar
5.Cameron, S., “Enhancing GJK: Computing Minimum and Penetration Distance Between Convex Polyhedra,” Proceedings of the IEEE International Conference on Robotics and Automation (1997) pp. 3112–3117.Google Scholar
6.Akgunduz, A., Banerjee, P. and Mehrotra, S., “A linear programming solution for exact collision detection,” J. Comput. Inform. Sci. Eng. 5, 48–55 (2005).CrossRefGoogle Scholar
7.Kitamura, Y., Smith, A., Takemura, H. and Kishino, F., “A real-time algorithm for accurate collision detection for deformable polyhedral objects,” Presence 7 (1), 36–52 (1997).CrossRefGoogle Scholar
8.Jimenez, P., Thomas, F. and Torras, C., “Collision Detection Algorithms for Motion Planning,” In: Robot Motion Planning and Control, Lecture Notes in Control and Information Science, Vol. 229 (Laumond, J.-P. ed.) Chapter 6. (1998) pp. 305–343.CrossRefGoogle Scholar
9.Wang, W., Choi, Y. K., Chan, B., Kim, M. S. and Wang, J., “Efficient collision detection for moving ellipsoids using separating planes,” Computing 72, 235–246 (2004).CrossRefGoogle Scholar
10.Rimon, E. and Boyd, S. P., “Obstacle collision detection using best ellipsoid fit,” J. Intell. Robot. Syst. 18, 105–126 (1997).CrossRefGoogle Scholar
11.Ju, M.-Y., Liu, J.-S., Shiang, S.-P., Chien, Y.-R., Hwang, K.-S. and Lee, W.-C, “Fast and accurate collision detection based on enclosed ellipsoid,” Robotica 19, 381–394 (2001).CrossRefGoogle Scholar
12.Jimenez, P., Thomas, F. and Torras, C., “3D collision detection: A survey,” Comput. Graph. 25 (2), 269–285 (2001).CrossRefGoogle Scholar
13.Fares, C. and Hamam, Y., “Collision Detection for Rigid Bodies: A State of the Art Review,” 15th International Conference on Computer Graphics and Applications (GraphiCon'2005), Russia (2005).Google Scholar
14.Lin, M. C., “Efficient Collision Detection for Animation and Robotics,” PhD Thesis (University of California, Berkeley, 1993).Google Scholar
15.Forbes, K., “Motion Curves: A Versatile Representation for Motion Data,” MS Thesis (Graduate Department of Computer Science, University of Toronto, Crescent Toronto, Ontario, Canada, 2005).Google Scholar
16.Ong, C. J. and Gilbert, E. G., “Growth distances: New measures for object separation and penetration,” IEEE Trans. Robot. Autom. 12 (6), 888–903 (1996).Google Scholar
17.Gilbert, E. G., Johnson, D. W. and Keerthi, S. S., “A fast procedure for computing the distance between complex objects in three-dimensional space,” IEEE Trans. Robot. Autom. 4, 193–203 (1988).CrossRefGoogle Scholar
18.Inui, M., Miura, M. and Kimura, F., “Positioning conditions of parts with tolerance in an assembly,” Proceedings of the IEEE International Conference on Robotics and Automation (1996) pp. 2202–2207.Google Scholar
19.Inui, M., “Tolerance Analysis of Mechanisms Using Dynamic, Simulation Method,” Nihon Kikai Gakkai Kanto Shibu. Seimitsu Kogakkai Ibaragi Koenkai Koen Ronbunshu, Vol. 1999 (The Japan Society of Mechanical Engineers Kanto Branch, Japan, 1999) pp. 119–120.Google Scholar
20.LaValle, Steven M., Planning Algorithms (Cambridge University Press, Cambridge, UK, 2006).CrossRefGoogle Scholar
21.Xiao, J. and Ji, X., “Automatic generation of high-level contact space,” Int. J. Robot. Res. 20 (7), 584–606 (2001).CrossRefGoogle Scholar
22.Pan, W.-H., Liu, J.-S. and Ku, W.-Y., “Fast collision detection method for the scaled convex polyhedral objects with relative motion,” Proceedings of the IEEE International Symposium on Assembly and Manufacturing, Ann Arbor, Michigan (2007) pp. 184–190.Google Scholar
23.Yang, F. and Marefat, M. M., “Achieving desired contact state transitions of polyhedral objects with compliant motions,” Proceedings of the IEEE International Conference on Robotics and Automation (2005) pp. 4206–4211.Google Scholar
24.Tsai, L.-W., Robot Analysis (John Wiley, New York, 1999).Google Scholar
25.Goeree, B. B., Fasse, E. D. and Marefat, M. M., “Determining feasible contact state of pairs of spatial polyhedra,” Proceedings of the IEEE International Conference on Robotics and Automation (2000) pp. 1396–1401.Google Scholar
26.Goeree, B. B., Fasse, E. D. and Marefat, M. M., “Verifying contact hypotheses of planar polyhedral objects using penetration growth distance,” Robot. Comput. Integr. Manuf. 17, 233–246 (2001).CrossRefGoogle Scholar
27.Hong, S.-M., Yeo, J.-H. and Park, H.-W., “A fast procedure for computing incremental growth distance,” Robotica 18, 429–441(2000).CrossRefGoogle Scholar
28.Choi, Y.-K., Li, X., Rong, F., Wang, W. and Cameron, S., “Determining the directional contact range of two convex polyhedra,” Comput. Aided Des. 42, 27–35 (2010).CrossRefGoogle Scholar
29.Je, C., Tang, M., Lee, Y., Lee, M. and Kim, Y. J., “PolyDepth: Real-time penetration depth computation using iterative contact-space projection,” ACM Trans. Graph. 31 (1) Article 5, 1–14 (Jan. 2012).CrossRefGoogle Scholar